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• W3099701903 abstract "We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include new proofs of Krcatovich's result that knots with $L$-space surgeries are prime and Hedden and Watson's result that the rank of knot Floer homology detects the trefoil among knots in the 3--sphere. We also generalize the latter result, proving a similar theorem for nullhomologous knots in any 3--manifold. We note that our method of proof inspired Baldwin and Sivek's recent proof that Khovanov homology detects the trefoils. As part of this work, we also introduce a numerical refinement of the Ozsv'ath-Szab'o contact invariant. This refinement was the inspiration for Hubbard and Saltz's annular refinement of Plamenevskaya's transverse link invariant in Khovanov homology." @default.
• W3099701903 created "2020-11-23" @default.
• W3099701903 creator A5051949965 @default.
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• W3099701903 date "2018-10-18" @default.
• W3099701903 modified "2023-09-29" @default.
• W3099701903 title "A note on the knot Floer homology of fibered knots" @default.
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• W3099701903 doi "https://doi.org/10.2140/agt.2018.18.3669" @default.
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